Gurkan Yildirim, 25, got into the car in a street near the Australian International Academy in Coburg North on November 8, 2016, while its owner - the baby's mother - was standing nearby talking to a friend.

The mother, who was waiting to pick up her children from school, left the car's engine running and the windows down because her daughter was still asleep, court documents say.

She said she put her older son in her friend's car so as not to wake her, and checked on her a number of times.

CCTV footage shows Yildirim and another man got into the car, locked the doors, and drove off as the baby's mother and her friend hit the car with their hands and yelled "There's a baby in the car!"

The mother told police that Yildirim - who was on bail at the time - should have seen the child seat and the baby's toys through the open car windows.

A friend of the mother, Elecia Arasan, leapt onto the bonnet of the car as it drove away but fell off after the car hit a van at a nearby intersection.

Yildirim, who reportedly denied his involvement in the incident after he was initially arrested, pleaded guilty to a number of crimes on Tuesday including taking away a child under 16, unlawfully imprisoning her against her will and reckless conduct placing the woman in danger of death, at the Melbourne Magistrates Court after he was committed to stand trial.

He also pleaded guilty to stealing the car, committing the crimes on bail, damaging property, driving a car in a dangerous manner, driving while disqualified, failing to stop immediately after accident and failing to give his name and address at the scene of an accident.

A witness told police that a man approached him later that afternoon near a Brunswick alley, begging for his help, court documents say.

The man told him: "There's a baby in the back ... I've just stolen a car" and later fled the scene.

The witness told police he could hear the baby screaming before he even reached the car. He waved down a car, whose driver helped him call the police.

Fairfax Media has previously reported that a 44-year-old Hadfield man was also charged with stealing the car last year.

Magistrate Suzanne Cameron remanded Yildirim to appear at a pre-sentence hearing at the County Court on July 21.